Centralized and Decentralized Global Outer-synchronization of Asymmetric Recurrent Time-varying Neural Network by Data-sampling

TL;DR

This paper establishes conditions under which asymmetric recurrent time-varying neural networks achieve outer-synchronization using data sampling, ensuring convergence and avoiding Zeno behavior, with practical numerical validation.

Contribution

It introduces new sufficient conditions for synchronization of asymmetric neural networks via centralized and decentralized data sampling methods, ensuring positive sampling intervals.

Findings

Synchronization conditions guarantee convergence of trajectories.

Positive lower bounds for sampling intervals prevent Zeno behavior.

Numerical example confirms theoretical results.

Abstract

In this paper, we discuss the outer-synchronization of the asymmetrically connected recurrent time-varying neural networks. By both centralized and decentralized discretization data sampling principles, we derive several sufficient conditions based on diverse vector norms that guarantee that any two trajectories from different initial values of the identical neural network system converge together. The lower bounds of the common time intervals between data samples in centralized and decentralized principles are proved to be positive, which guarantees exclusion of Zeno behavior. A numerical example is provided to illustrate the efficiency of the theoretical results.